Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. II. Multivariant phase transformations and stress space analysis

Abstract

In this paper, the three-dimensional Landau model of austenite-martensite transformations constructed in Part I is generalized to include transformations between an arbitrary number of martensitic variants. The model can incorporate all temperature-dependent thermomechanical properties of both phases for arbitrary crystal symmetries, including higher-order elastic constants, and it correctly describes the characteristic features of stress-strain curves for shape-memory alloys and steels, namely, constant transformation strain tensors, constant or weakly temperature dependent stress hysteresis, and transformation at nonzero tangent moduli. Geometric representations of the conditions for phase equilibrium and phase transformations in six-dimensional stress space are developed. For the cubic-tetragonal phase transformation, equilibrium and transformation surfaces in three-dimensional stress space and the corresponding lines in the deviatoric-stress plane are found at various temperatures, and transformation processes are analyzed. All model parameters are obtained for the NiAl cubic-tetragonal phase transformation using the results of molecular dynamics simulations available in the literature.